a+b>c,a、b、c>0 求证a^3+b^3+c^3+3abc>2(a+b)c^2
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a+b>c,a、b、c>0 求证a^3+b^3+c^3+3abc>2(a+b)c^2
a+b>c,a、b、c>0 求证a^3+b^3+c^3+3abc>2(a+b)c^2
a+b>c,a、b、c>0 求证a^3+b^3+c^3+3abc>2(a+b)c^2
左=(a+b)*(a^2+b^2-ab)+c^3+3abc>(a^2+b^2-ab)*c+c^3+3abc=c*[(a+b)^2+c^2]>=c*2*(a+b)*c=右
左=(a+b)*(a^2+b^2-ab)+c^3+3abc>(a^2+b^2-ab)*c+c^3+3abc=c*[(a+b)^2+c^2]>=c*2*(a+b)*c=右
=(a+b)*(a^2+b^2-ab)+c^3+3abc>(a^2+b^2-ab)*c+c^3+3abc=c*[(a+b)^2+c^2]>=c*2*(a+b)*c=右